A slight majority of Minnesota voters expressed disapproval of President Obama’s health care law, known as Obamacare, according to a poll commissioned by the conservative Minnesota Jobs Coalition.

The partly automated telephone poll of 400 likely voters, conducted this week by the Tarrance Group, found that 51 percent disapprove of the law, compared to 43 percent who approve. Strong opposition stood at 43 percent, compared to strong support at 29 percent.

The poll, coming in the midst of a very shaky rollout for the new health care law, reflected strong partisan differences. But, tellingly, independents broke against the law 2 to 1, the poll found.

The poll did not measure how many of those who said they dislike the law did so because of problems with the government Web site or because they would like to see its provisions go farther.

The same poll found diminished support for Sen. Al Franken, with 45 percent saying he deserves reelection next year, compared to 43 percent who say it’s time to “give a new person a chance.”

A Public Policy Polling survey last month found Franken’s approval rating among registered voters in Minnesota is at 51/43, almost identical to his 51/42 approval rating in their polls last May.

Public Policy Polling is generally regarded as a Democratic firm; Tarrance is more commonly used by Republicans.

The Tarrance poll found voters more evenly divided on Gov. Mark Dayton. It found 45 percent saying he deserves reelection, versus 45 percent who would like to give someone else a chance.

The poll, which also found that 60 percent of Minnesota voters think the country is headed down the “wrong track,” included both automated calls to landlines and live calls to cell phones. It had a margin of error of plus-or-minus 5 percent.